Both classes of reconstruction method work significantly better when used with orthogonal pattern sets, for example Hadamard matrices [1]}, [2]}, [3]}, where each mask probes a subset of spatial frequencies. For offline methods this is equivalent to ensuring full row rank, which increases the stability of the matrix inversion results. For TGI, it ensures that each pattern's spatial frequencies are counted democratically in the mean correction term. Either way, in the absence of noise, the result approaches the true image when the number of orthogonal patterns equals the number of pixels.
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